{
  "id": "0903.2363",
  "version": "v2",
  "published": "2009-03-13T12:01:28.000Z",
  "updated": "2011-02-08T13:12:45.000Z",
  "title": "Idempotent states on compact quantum groups and their classification on U_q(2), SU_q(2), and SO_q(3)",
  "authors": [
    "Uwe Franz",
    "Adam Skalski",
    "Reiji Tomatsu"
  ],
  "comment": "32 pages; version 2 revises the terminology, adds a few new results in Section 3 and introduces several minor corrections. The paper will appear in the Journal of the Noncommutative Geometry",
  "journal": "Journal of Noncommutative Geometry, Volume 7, Issue 1, 2013, pp. 221-254",
  "doi": "10.4171/JNCG/115",
  "categories": [
    "math.OA",
    "math.QA"
  ],
  "abstract": "Unlike for locally compact groups, idempotent states on locally compact quantum groups do not necessarily arise as Haar states of compact quantum subgroups. We give a simple characterisation of those idempotent states on compact quantum groups which do arise as Haar states on quantum subgroups. We also show that all idempotent states on the quantum groups U_q(2), SU_q(2), and SO_q(3) (q in (-1,0) \\cup (0,1]) arise in this manner and list the idempotent states on the compact quantum semigroups U_0(2), SU_0(2), and SO_0(3). In the Appendix we provide a short new proof of coamenability of the deformations of classical compact Lie groups based on their representation theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-08T13:12:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "43A05",
      "46L65"
    ],
    "keywords": [
      "idempotent states",
      "haar states",
      "classification",
      "compact quantum subgroups",
      "compact quantum semigroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2363F"
    }
  }
}